Symmetry breaking in active and quantum fluids

Jorn Dunkel (MIT)

Active biological fluids, such as bacterial and other microbial suspensions, can exhibit several striking symmetry breaking phenomena, from the spontaneous formation of vortex lattices to the emergence of large-scale unidirectional flows. Borrowing ideas from classical pattern formation theory, I will discuss generalized Navier-Stokes (GNS) equations as an analytically tractable minimal model of stress-driven active fluids. The GNS equations permit exact stress-free bulk solutions in planar and curved geometries, including Abrikosov-type lattices in 2D and Beltrami flows in 3D. A triad analysis shows that the combination of a generic linear instability and a standard advective nonlinearity can give rise to spontaneous chiral symmetry breaking that supports inverse energy transport in 3D. In the second part, we extend the underlying concepts to quantum fluids by deriving a higher-order generalization of the Gross-Pitaevskii model to study supersolid crystals and quasi-crystals. The analytical tractability of this framework is illustrated by determining the ground state phase diagram and the dispersion relations for supersolid lattice vibrations.